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A large number of water drops each of rdius r combine to have a drop of radius R. If the surface tension is T and the mechanical equivalent at heat is J then the rise in tempreature will be

A. 2T / rJ B. 3T /RJ C. $ {3J \over J } \left( { 1 \over r} - {1 \over R } \right) $ D. $ {2T \over J } \left( { 1 \over r} - {1 \over R } \right) $

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Explanation

Rise in tempreture $ \triangle \theta = { 3T \over Jsd } \left( {1 \over r } - { 1 \over R} \right) $ $ \triangle \theta = { 3T \over J} \left( {1 \over r } - { 1 \over R} \right) $ (For water S = 1 and d = 1)

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When liquid medicine of desting S is to be put in the eye. It is done with the help of a dropper as the bulb on the top of the dropper is pressed a drop forms at the opening od the dropper we wish to estimate the size of the drop. We dirst assume that the drop formed at the opening is spherical because the requires a minimum increase in its surface energy. To determine the size we calculate the net vertical force due to surface tension T when the radius od the drop is R. When this force becomes smaller than the weight of the drop the drop gets detched from the dropper. If the radius od the opening od the dropper is r ; the vertical force due to the surface tension onthe drop of radius R. (assuming r << R) is

A. $ 2 \pi r T $ B. $ 2 \pi R T $ C. $ { 2 \pi r^2 T \over R} $ D. $ { 2 \pi R^2 T \over r} $

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Explanation

Due to surface tension vertical force on drop $ Fv = T_2 \pi r Sm \theta $ $ = T_2 \pi r { r \over R} = T {2 \pi r^2 \over R } $

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When liquid medicine of desting S is to be put in the eye. It is done with the help of a dropper as the bulb on the top of the dropper is pressed a drop forms at the opening od the dropper we wish to estimate the size of the drop. We dirst assume that the drop formed at the opening is spherical because the requires a minimum increase in its surface energy. To determine the size we calculate the net vertical force due to surface tension T when the radius od the drop is R. When this force becomes smaller than the weight of the drop the drop gets detched from the dropper. .$ If l = 5 \times 10^ {-4} m, \rho = 10^ 3 kg m^{-3} = 10 ms ^ {-2 } T = 0.11 N m^{-1} $ the radius of the drop when it detaches from the dropper is approximately

A. $ 1.4 \times 10^{-3} m $ B. $ 3.3 \times 10^{-3} m $ C. $ 2.0 \times 10^{-3} m $ D. $ 4.1 \times 10^{-3} m $

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Explanation

$ { 2 \pi r^2 \over R } T = \rho { 4 \over 3} \pi R^3 .9 $

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When liquid medicine of desting S is to be put in the eye. It is done with the help of a dropper as the bulb on the top of the dropper is pressed a drop forms at the opening od the dropper we wish to estimate the size of the drop. We dirst assume that the drop formed at the opening is spherical because the requires a minimum increase in its surface energy. To determine the size we calculate the net vertical force due to surface tension T when the radius od the drop is R. When this force becomes smaller than the weight of the drop the drop gets detched from the dropper. After the drop detaches its surface energy is

A. $ 1.4 \times 10 ^ {-6 } J $ B. $ 2.7 \times 10 ^ {-6 } J $ C. $ 5.4 \times 10 ^ {-6 } J $ D. $ 8.1 \times 10 ^ {-6 } J $

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Explanation

$ U = T - A = 0.11 \times 4 \pi ( 1.4 \times 10 ^ {-3} )^2 $

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Assertion & Reason type questions Read the assertion and reason carefully and mark the correct option given below. Assertion : When height of a tube is less then liquid rise in the capillary tube the liquid does not overtow. Reason : Product of radius of meniscus and height of liquid incapilling tube always remains constant.

A. If both assertion and reason are true and the reason is the correct explanation of the assertion B. If both assertion and reason are true but reason is not the correct explanation of the assertion. C. If assertion is true but reason is false. D. If the assertion and reason both are false.

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Explanation

$ h = { 2T \over Rdg } \Rightarrow hR= { 2T \over dg } $ $ \therefore hR =constant $ Hence whenthe tube is of insufficient length radius of curvature of the liquid meniscus increassesso as to maintain the product hR a finite constant. i.e. as h decreases R increases and the liquid meniscus becomes more and more flat but the liquid does not overflow.

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Assertion & Reason type questions Read the assertion and reason carefully and mark the correct option given below. Assertion : The concept of surface tension is help only for liquids. Reason : Surface tension does not hold for gases.

A. If both assertion and reason are true and the reason is the correct explanation of the assertion B. If both assertion and reason are true but reason is not the correct explanation of the assertion. C. If assertion is true but reason is false. D. If the assertion and reason both are false.

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Explanation

We know that the intermolecular distance between the gas moleculas is Large as compaired to that of liquid Due to it the forces of cohesion in the gas moleculas are very small and these are quite Large for liquids. Therefor the concept of surface tension is applicable to Liquid but not to gasses

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Assertion & Reason type questions Read the assertion and reason carefully and mark the correct option given below. Assertion : The water rises higher in a capillary tube of small diametre than in the capillary tube of large diamtre. Reason : Height through which liquid rises in a capillary tube is inversely proportional to the diameter of the capillary tube.

A. If both assertion and reason are true and the reason is the correct explanation of the assertion B. If both assertion and reason are true but reason is not the correct explanation of the assertion. C. If assertion is true but reason is false. D. If the assertion and reason both are false.

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Explanation

The height ofcapillary rise is inverslypropostional to radius (or diametre) of capillary tube i.e. $ h \alpha { 1 \over r } $ so, for smaller r the value of his higher

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Assertion & Reason type questions Read the assertion and reason carefully and mark the correct option given below. Assertion : Tiny drops of liquid resist deforming forces better than bigger drops. Reason : Excess pressure inside a drop is directly proportional to surface tension.

A. If both assertion and reason are true and the reason is the correct explanation of the assertion B. If both assertion and reason are true but reason is not the correct explanation of the assertion. C. If assertion is true but reason is false. D. If the assertion and reason both are false.

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Explanation

When a drop of Liquid is poured on a glass, plate, the shape of the drop also is governed the force of gravity for every small drops the potential energy due to gravity is insignification. Compared to that due to surface tention. Hence, in this case the shape ofthe drop is determined bysufrace tension alone and drope becomes spherical.

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When a large bubble rises drom the bottom of a lake to the surface. Its radius double S. It atmospheric pressure in euqal to that of colurnn of colurnn of water height H then the depth of Lake is

A. H B. 2H C. 7H D. 8H

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Explanation

$ p_1 v_1 = p_2 v_2 $ $ ( p + h \rho g ) {4 \over 3} \pi r^3 = p_0 \times {4 \over 3} (2 r)^3 $

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A triangular lamind of area A and, height h is immersed in a liquid of density S in a vertical plane with its base on the surface of the liquid. The thrust on lamina is

A. $ {1 \over 2 } A \rho gh $ B. $ {1 \over 3 } A \rho gh $ C. $ {1 \over 6 } A \rho gh $ D. $ {2 \over 3 } A \rho gh $

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Explanation

$ Thrust on lamina = pressure at centroid \times area $ $ = { h \rho g \over 3 } \times A = {1 \over 3 } A \rho gh $

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